OK, I posted the question (not published yet - waiting to be moderated).
I found the answer. It probably has to do with the number of features in Max, confusing for the beginner user like myself.

So the reason for this error is because if I want to convert file (CD, AIFF or other) to AAC format I need to choose the Apple Mpeg-4 file which is the container and then select AAC format. Alternatively choosing Mpeg-4 Audio would also work.

Selecting AAC as container and Mpeg-4 as file format doesn't convert and produces the error "The call to AudioConverterSetProperty failed."